Question

What is the property of two vectors if A+B=A-B

Answer 1

they are perpendicular to each other

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Answer 2

Given that,

Vectors, $A+B=A-B$

To find,

The property of vector.

Solution,

Let, $|A+B|=|A-B|$

Squaring both sides on above equation,

$A^2+B^2+2AB\cos \theta=A^2+B^2-2AB\cos \theta\\\\2AB\cos \theta+2AB\cos \theta=0\\\\4AB\cos \theta=0$

It gives,

$\cos\theta=0\\\\\theta=90^{\circ}$

If  $|A+B|=|A-B|$, then it shows that A and B are perpendicular to each other.

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